A first-class approach of higher derivative Maxwell–Chern–Simons–Proca model

Abstract

The equivalence between a higher derivative extension of Maxwell-Chern-Simons-Proca model and some gauge invariant theories from the point of view of the Hamiltonian path integral quantization in the framework of the gauge-unfixing approach is investigated. The Hamiltonian path integrals of the first-class systems take manifestly Lorentz-covariant forms.

Aspects of degrees of freedom in higher derivative massive electromagnetic theories

“…The next step is to verify whether the real and unequal roots are all positive. It has been proved in [2,4,11] that for and the three distinct real roots of the equation (7) In order to analyze the absence or presence of the ghosts excitations we need to investigate the signs of the residues at each simple pole of the propagator. In the case of MTCSP model, not all residues have the same sign and therefore the MTCSP model is plagued by ghosts [4].…”

“…First model is constructed by replacing the topological Chern-Simons term with a third order derivative extension of itself [1] in Maxwell-Chern-Simons-Proca [2,3] ( 1 ) with , and real constants [4].…”

BF quantization of MCS Proca model

“…In order to do this, we start from the first-class system constructed in the above and impose the canonical gauge condition 0. (18) while the first-class Hamiltonian takes the form…”

“…The quantization procedure relies on the path integral of a first-class system equivalent with the original theory. In view of this we construct a first-class system equivalent with the original second-class theory using the BF method and then we quantify the resulting first-class system [6][7][8][9][10][11][12][13][14][15][16][17][18]. In [5], starting from MCS Proca model, it is constructed an equivalent first-class model using gauge-unfixing method.…”

On the quantization of the massive forms

“…After an appropriate extension of the phase-space, some field redefinitions, and performing some partial integrations over the auxiliary fields we find out that the argument of the exponential from Hamiltonian path integral of the first-class system takes the form [15], [16] …”